A linear conflict-controlled process of two players with a terminal set in the form of the sum of a linear subspace and a convex compact in its orthogonal complement is considered. The process is considered from the point of view of the first player. Its goal is to bring the controlled object to the terminal set. It is assumed that the first player knows the dynamic characteristics of the controlled object, the phase variables and the control of the second player. Sufficient conditions are presented under which the first player can guarantee the bringing of the phase vector of the game to the terminal set. A form of positional counter-control of the first player guaranteeing the completion of the process is given. Such positional counter-control is intended for operation in the logic of step-by-step positional control of a combined system including a real controlled object and a model (guide) and implementing tracking of the guide's movement in the form of an extreme aiming procedure implemented step-by-step in a discrete system and having resistance to information interference, achieved in a scheme with a guide. Examples are considered.
Keywords: differential games, positional control, counter-control, positional counter-control, object bringing problem, structural synthesis, guide control, analytical design of aggregated controllers
Received January 17, 2025
Revised April 14, 2025
Accepted April 21, 2025
Funding Agency: The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2022-284 and state-funded research topic № 5.4 of the Faculty of Computational Mathematics and Cybernetics of the Moscow State University.
Nikolay Leontievich Grigorenko, Dr. Phis.-Math Sci., Faculty of Computational Mathematics and Cybernetics of the Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: grigor@cs.msu.ru
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Cite this artile as: N.L. Grigorenko. On linear differential games of pursuit in the class of positional countercontrols. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 2, pp. 69–80.
